Question

X is a Poisson random variable with a mean of 10,

a)What is the probability that x is equal to 8 (round to four decimal places)?

b) What is the probability that x is greater than or equal to 2 (round to four decimal places)

Answer 1

Solution :

Given that ,

mean = = 10

Using Poisson probability formula,

P(X = x) = (e^- * ^x ) / x!

a)

P(X = 8) = (e^-10 * 10⁸⁾ / 8!

= 0.1126

The probability that x is equal to 8 is 0.1126

b)

P(X 2) = 1 - P(X < 2)

= 1 - ( P(X = 0) + P(X = 1) )

= 1 - ( (e^-10 * 10⁰⁾ / 0! + (e^-10 * 10¹⁾ / 1! )

= 1 - ( 0 + 0.0005)

= 0.9995

The probability that x is greater than or equal to 2 is 0.9995